Project Summary Periodontitis, which can result in tooth loss, is a serious gum disease and public health concern. Periodontitis progression is usually measured using multiple clinical outcomes on each tooth per patient over time. Thus, statistical models used to analyze periodontitis progression need to account for the multiple correlation structures: the correlation between teeth within each patient and the correlation between temporal observations on the same patient. Further, when a patient?s periodontitis progression is monitored over time, the number of observations tends to decrease due to the patient?s losing teeth, resulting in another analytical challenge. Current statistical methods to analyze dental studies, including periodontitis progression, need further development to accommodate a more complex data structure. To advance periodontitis research, and motivated by the limited availability of statistical methods to model the effect of time-dependent covariates on multiple outcomes including ordinal variables while properly accounting the multiple correlation structures, we propose the following three specific aims as the research component of the fellowship training: (1) Extend existing methods to model longitudinal ordinal outcomes; (2) Extend existing methods to jointly model multiple outcomes; and (3) Extend existing methods to analyze time-dependent covariates. For each aim, we will (a) develop models based on existing methods, (b) perform simulation studies to evaluate the model performance, and (c) apply each of our proposed methods to analyze a data set from a real longitudinal dental study. We will make the proposed methods easily accessible to statisticians and dental health professionals by publishing our results in biostatistical and dental health journals, presenting our results at statistical and dental conferences, and uploading the programming code onto a public website. The proposed research will help advance the field of dental research by allowing researchers to use complex dental data efficiently and to properly account for multiple correlation structures.